Vibrating structure gyroscopes, fabricated using Micro-Electro-Mechanical Systems (MEMS) technology, are finding use in aerospace applications for guidance and control. A typical Coriolis-type vibrating structure gyroscope comprises an annular resonator supported by compliant legs to vibrate in-plane in response to electrostatic drive signals. The annular resonator can be operated using a cos 2θ vibration pair, e.g. as described in WO 2006/006597. In operation, a drive transducer excites a primary carrier vibration along a primary axis of motion at a nominal resonant frequency e.g. 14 kHz. When the gyroscope is rotated around an axis normal to the plane of the annular resonator, Coriolis forces are generated which couple energy into a secondary response vibration along a secondary axis of motion oriented at 45° to the primary axis. In the theoretical case of a perfectly annular resonator, depicted schematically in FIG. 1, the primary motion is always aligned to the primary axis regardless of the frequency of excitation. The Coriolis-induced secondary response vibration is aligned to the secondary axis at 45° and there is no frequency split.
However, in reality there are geometrical imperfections in the annular shape of the resonator and this means that the primary carrier vibration at a given resonant frequency (e.g. 14 kHz) is a superposition of two orthogonal modes, a high frequency mode (HFM) shifted to a slightly higher frequency fH and a low frequency mode (LFM) shifted to a slightly lower frequency fL. As imperfections lead to the modes having different frequencies, one is inevitably higher frequency than the other. However the higher mode frequency fH may or may not be higher than the perfect case where the mode frequencies are the same. The frequency split Δf is the difference between the frequencies of the HFM and LFM, i.e. Δf=fH−fL. For a cos 2θ vibration pair, the orthogonal high frequency and low frequency modes are always at 45° to each other but can be at any arbitrary angular position α relative to the primary axis typically used as a reference axis. The value of the angle α will depend on the imperfections in the resonator.
MEMS design and fabrication processes are capable of producing planar silicon ring resonators with fine tolerances in an attempt to minimise any frequency difference between the high frequency and low frequency modes. However, even small imperfections in the geometry of an annular resonator will typically give rise to a residual frequency split.
Performance of MEMS ring gyroscopes can be improved by more accurate balancing of the high frequency and low frequency modes than can be achieved at manufacture. In one approach, the mass or stiffness distribution of the annular resonator is adjusted, for example using laser removal of material post-manufacture. Laser balancing, as described in WO 2013/136049, is typically used as part of the production process for inductive gyroscopes. This gives improved performance but cannot account for any variation during operation and life.
In capacitive gyroscopes, electrostatic balancing schemes typically use a number of balancing electrode plates arranged around the annular resonator so that balancing can be resolved to any position around the ring. An initial, static electrostatic balance correction can be applied to one or more of the plates to locally adjust the stiffness of the annular resonator and compensate for manufacturing tolerances. However it is also known to control the electrostatic balancing voltages during operation. For example, WO 2006/006597 describes sixteen balancing electrode plates used for vibrational frequency adjustment during operation of the gyroscope. Electrostatic balancing applies a local reduction in stiffness which produces a frequency reduction proportional to the square of the voltage difference between the ring and the balancing plate. This means that the high frequency and low frequency modes can be differentially adjusted to try to achieve accurate matching. By applying fixed DC voltages to a group of four of the balancing plates located around the annular resonator, the frequency split Δf can be reduced to less than 1 Hz. There is seen in FIG. 2 an example of a 33,000 Q factor gyroscope having a 0.424 Hz split between the frequencies of the HFM and LFM (α=0°).
Although electrostatic balancing has been used with capacitive gyroscopes, the digitally-controlled voltages applied to the balancing plates have discrete analog output values set by the digital-to-analog converter (DAC) and its defined LSB (least significant bit), i.e. the step between successive analog outputs. When using digital means of linearly varying the voltage, the resolution of the balancing effect decreases with increasing applied voltage difference. This is due to the squared nature of balancing, with the frequency split Δf being related to the voltage squared. If a dynamic balancing is implemented, combined with a large static balance correction, the available resolution is degraded, which limits the overall gyroscope performance.
There remains a desire to achieve improved electrostatic frequency balancing during operation of a capacitive gyroscope.